Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ev_app

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {V : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} V] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          [inst_3 : CategoryTheory.MonoidalCategory V] →
            [inst_4 : CategoryTheory.MonoidalClosed V] →
              {F G H : CategoryTheory.Functor C V} →
                [inst_5 : CategoryTheory.MonoidalCategory.DayConvolution F H] →
                  CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H →
                    (CategoryTheory.MonoidalCategory.DayConvolution.convolution F H ⟶ G)

Given ℌ : DayConvolutionInternalHom F H, if we think of H.obj G as the internal hom [F, G], then this is the transformation corresponding to the component at G of the "evaluation" natural morphism F ⊛ [F, _] ⟶ 𝟭.

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed

Cited by

5 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.MonoidalCategory.DayConvolution